Why Schools Need a Phonics-Style Reckoning for Math
Yglesias: Teachers should embrace showing kids how to tackle problems — and then make them practice until they get good at it on their own.
A version of this essay appeared on Matthew Yglesias’ , a site dedicated to offering pragmatic takes on politics and public policy
At this point, everyone who cares about education policy at all has probably, or pretends to have, and is aware that there is a correct way to teach children to read and also a different way that dominated education schools for a generation. There are now many state- and city-level pushes to institute correct instructional practices grounded in “the science of reading,” and the main question is about rather than what the practice should look like.
I think it’s less understood that this specific fiasco in early literacy was downstream of the education theory world’s broader turn against explicit instruction.
This has always struck me as a bit odd because “teaching things to people” is of course a human endeavor that exists outside the context of “being a K-12 teacher.” And it seems to me that outside of school, explicit instruction is the dominant instructional method.
I once took a knife skills class, and they just show you how to chop an onion. You trim the stem. You cut in half from end to end. You peel the skin. You make vertical slices that leave the root intact, then horizontal slices, and then another set of vertical slices across the third dimension. Here’s a from “The Art of Manliness.” There are also many videos demonstrating this method.
There is a specific, correct way to do this, and part of learning to cook is being told how to do it.
A person with excellent spatial reasoning could probably figure this out from first principles given an onion and a knife. But the normal way to learn to chop is to be explicitly shown. Chopping a bell pepper is a little different, but you can be shown that, too. You don’t just give people knives and tell them to experience the joy of chopping. Because even though some people really love cooking and find it to be an amazing avenue for self-expression, it’s also useful to know how to chop vegetables, and the best way to get from zero to vaguely competent is to be taught the proper way to do it and then given the opportunity to practice.
Education school theorists, for reasons that are disputed, seem to dislike this idea.
From Jean-Jacques Rousseau’s “Emile” to Paulo Freire’s “The Pedagogy of the Oppressed,” a long tradition in the field mashes up romanticism with left-wing politics and sentimentality about the point of school to suggest that there’s some other, secretly better way of teaching things to beginners than just literally teaching them.
But while there’s certainly more to life than explicitly instructing novices in the basics, across a huge range of domains, that really is the foundation of knowledge. You need to master sounding words out before you can analyze literature, and it’s extremely helpful to have your times tables and other basic math facts memorized so that your brain can think about more elevated mathematical questions without constantly tripping over the calculations.
Learning is fundamental
The association between fuzzy educational practices and left-wing politics strikes me as rather contingent.
The Soviet Union and its satellite states in Eastern Europe, for example, all ran school systems that would read as strikingly “right-wing” by American standards (of course, these regimes weren’t exactly defunding the police, either). Antonio Gramsci also about elementary education.
But in the contemporary West, a constellation of odd pedagogical notions has a very particular ideological alignment.
The influential Stanford education professor Jo Boaler the habit of “present[ing] mathematics procedurally, as sets of steps to memorize and apply” and “times table repetition, practice, and timed testing is unnecessary and damaging.” As early as 2013, she was that there’s too much “drill and practice” in math education.
Efforts to stigmatize the basic building blocks of teaching and learning have at times taken pretty loopy turns. There was a big national news story five years ago when an outfit called Equitable Math was arguing that focusing on getting the right answer was.
In their less loopy forms, though, the ideas flying under the banner of “discovery,” “constructivist,” or “inquiry-based” math offer high-minded justifications about allowing children to unearth the deeper truths of the mathematical world for themselves through play and free inquiry rather than by drilling algorithmic procedures for solving problems.
There is doubtless room for this sort of inquiry, especially when you want more advanced students to achieve a deeper understanding. But instruction with minimal guidance simply does not work ().
And while there’s something to the concept of “” versus simply telling kids how to solve the problem, it can also easily become an excuse for not actually teaching kids how to do the math.
Practice makes perfect
In particular, I would say that Boaler’s narrative about the perils of over-drilling seems to come from a counterfactual universe in which everyone is learning basic math well and then stalling out. That does happen sometimes! Probably all of us who’ve learned math at some point hit a point at which the material is just too hard for us. And the question of how to keep people motivated to work through the pain and genuinely get as far as they can is interesting.
But the actual situation in American math education is that in 2019, just 50% of eighth graders taking the National Assessment of Educational Progress math assessment got this word problem correct, and by 2022,.

This is just not that deep of a question. Apparently, a very large share of American eighth graders cannot reliably do division. If you present mathematics procedurally, as sets of steps to memorize and apply, then I think kids are going to be able to answer this question.
Beyond galaxy brain ideology, hostility to explicit instruction seems downstream of labor union politics.
Teachers’ unions in the United States, like labor unions generally, favor salary structures that are heavily weighted toward the interests of the most senior union members. As a result, they push for compensation schemes that are heavily backloaded (generous pensions and health plans relative to actual salaries) and where salaries are based pretty strictly on seniority rather than on teaching skill, outside labor-market options, or compensating differentials for harder assignments.
It’s not unusual for public-sector collective-bargaining agreements to have undesirable features for no good reason (see the that are being). But K-12 education is unusual in that it’s the subject of much more public discussion — parents understandably have a lot of opinions — so union leaders can’t just defend their position by saying, “Well, that’s how our members want it.”
They need to come up with reasons for why the system should work the way their most senior members want it to work.
This has meant, over the course of my career, a tremendous amount of effort to discredit the idea of giving students standardized tests as a way of measuring their subject matter competency. There’s been a lot of emphasis on the idea that but also a broader effort to discredit the idea that teachers whose students improve on tests are doing a good job of teaching.
As long as I’ve been covering these issues, union leaders have been raising the specter of “” (that’s from 2003) as a classroom practice. The National Education Association is constantly warning of the dangers of “,” Randi Weingarten, and I think it’s just remarkably obfuscatory. One can, of course, imagine a classroom that is overly focused on repetition and rote memorization relative to what I would consider an educational ideal.
But in a country full of classrooms like that, more than 44% of students could accurately answer the ribbon question.
You can literally just teach things
An interesting fact about modern human life is that while “education” happens within a specific set of institutions, “learning things” occurs in a much broader set of contexts. And I think it’s striking that in non-school contexts, we invariably rely quite a bit on explicit instruction.
For example, I sometimes like to impress children with my limited-but-impressive-to-kids ability to juggle.
Invariably, when a kid tries to copy what they just saw, they can’t execute even a single toss. There is no amount of exploratory tossing of balls that will lead most children to figure out how to juggle — they’ll get frustrated and give up.
Yet learning to juggle is actually pretty easy. You need to start with three scarves and do. When you can do that really well (“drill and kill”), you can try it with a set of balls. If you get good at balls (drill and kill again), you can start tossing around apples or stuffed animals or other objects that are less perfectly balanced. I don’t know how to juggle clubs, because the drill-and-kill instructional methods I was taught did not impart a lifelong love of juggling. If you want to develop a really impressive juggling act, then at some point you’re going to have to go beyond drill and kill. But most people can’t juggle at all, and they could if they received explicit instruction and practiced.
My son is a competitive swimmer, and when his team practices, they do a good number of repetitive drills because the coaches are trying to get them to swim properly. Lots of kids love swimming for fun in the summer, but you’re not going to win a race unless you receive a lot of explicit instruction in exactly the right way to dive, to turn, to kick, and to hold your arms. Unstructured discovery is never in a million years going to lead a child to a biomechanically optimal freestyle, much less a legal butterfly.
He also used to be on a much more low-key soccer team. But the team still had practices, and the practices still had lots of explicit drilling. He also plays soccer for fun at recess, which is great. But if your team wants to win games, the players need explicit instruction in how to use their instep to control a pass and how to do a correct throw-in from the sidelines.
Imagine trying to learn how to tie a tie via “productive struggle” rather than just. That would be insane!
Now what’s true is that if you want to, you need to obtain a deeper comprehension of the relevant topology and probably do a fair amount of exploration. But just learning how to do a four-in-hand or a half-Windsor is really easy if someone teaches you and insanely frustrating if you’re left to flounder and figure it out on your own.
A disservice to everyone
Math professor Anna Stokke has been in the trenches battling bad math instruction techniques, and I strongly and on this.
But the basic point she’s making is really simple: Deep understanding is not generated through some separate teaching process that replaces drilling; it’s an outcome that comes several steps after mastering the basics. Whether it’s a tie knot or algebra, you need to learn how to do it first, then practice it until you’re fluent, and then you can explore.
One irony of unions and left-aligned institutions derogating practice and drills is that — like with progressive attacks on sorting students by ability — this approach in practice does a huge disservice to classroom teachers by saddling them with an impossible job.
Teaching is a complicated, multifaceted profession that is difficult under any circumstances.
But to the extent that we can simplify the actual content part of the job by giving the teacher a class of kids who are starting out in roughly the same place and then trying to impart a defined set of skills to them, the work is at least doable.
This is the reason why sports coaches and birthday party magicians and unemployed cooks are able to teach people how to swim the butterfly or juggle balls or cut an onion, even while middle-school math teachers are struggling to get kids to do division. You need to let the teachers just teach division!
One thing I didn’t convey as clearly as I wanted to in is that outside math tutors aren’t just being used by families in “bad” schools — by parents who’ve already moved to the upscale suburbs with the “good” schools. Just look at the D.C. suburbs:

There’s no big secret to what these private classes are doing; it’s just.

Kumon has not discovered some secret stash of super-teachers capable of feats beyond the comprehension of normal K-12 educators. The program just gives its instructors a feasible job: show kids how to do the problem and make them practice until they get good at it. We can do this in normal schools, too, but we have to let go of this paranoia around “drill and kill” and just be normal.
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